A new method for treating boundary-value problems in gas-kinetic theory has been developed. The new method has the advantage of reproducing the bulk or asymptotic flow properties accurately whilst giving a realistic description of the behaviour of the molecular distribution function in the neighbourhood of a wall. As an example, the Kramers, or slip-flow, problem is solved for a general specular-diffuse boundary condition and some new expressions for the slip coefficient, flow speed and molecular distribution function at the surface are derived.

A brief discussion of the eigenvalue spectrum of the associated Boltzmann equation is given and its physical significance pointed out.

Certain analogies between this problem and the Milne problem in neutron transport theory are demonstrated.

Onset times for convection induced by buoyancy forces have been measured. Results on three aqueous systems are summarized in terms of a critical value for a time-dependent Rayleigh number. Because of the presence of minute traces of unavoidable surface-active contaminants, a ‘free’ water surface behaved as if it were inflexible and laterally rigid so far as determining first convective motion was concerned. The form of the onset motion was observed with schlieren photography for both top and side view. The pattern at onset was frequently in the form of plunging rings. Surface effects were demonstrated with an organic liquid layer in which onset times were measured for convection driven by surface tension gradients as well as by buoyancy forces. The data are compared with some recent predictions of linear stability analyses.

‘Best’ solutions for the shock-structure problem are obtained by solving the Boltzmann equation for a rigid sphere gas by applying minimum error criteria on the Mott-Smith ansatz. The use of two such criteria minimizing respectively the local and total errors, as well as independent computations of the remaining error, establish the high accuracy of the solutions, although it is shown that the Mott-Smith distribution is not an exact solution of the Boltzmann equation even at infinite Mach number. The minimum local error method is found to be particularly simple and efficient. Adopting the present solutions as the standard of comparison, it is found that the widely used v2x-moment solutions can be as much as a third in error, but that results based on Rosen's method provide good approximations. Finally, it is shown that if the Maxwell mean free path on the hot side of the shock is chosen as the scaling length, the value of the density-slope shock thickness is relatively insensitive to the intermolecular potential. A comparison is made on this basis of present results with experiment, and very satisfactory quantitative agreement is obtained.

The paper presents the method of solving a class of two-dimensional problems of the similarity flow of an incompressible fluid with a free surface. The fluid is assumed to be non-viscous and weightless. We consider two-dimensional irrotational similarity flows with dimensionless hydrodynamic characteristics depending only on the ratios x/v0t, y/v0t, where x, y are Cartesian co-ordinates, t is time and v0 is a constant of the velocity dimension.

The proposed method is based upon using the function introduced by Wagner (1932) and can be applied to the problems where the flow region is bounded by free surfaces and uniformly moving (or fixed) rectilinear impermeable boundaries. Introduction of Wagner's function makes it possible to reduce each of the problems under consideration to a non-linear singular integral equation for the real function.

The method is illustrated by solving the classical problem of the uniform symmetrical entry of a wedge into a half-plane of a fluid.

The direct-simulation Monte Carlo procedure for the modelling of rarefied gas flows on a digital computer has been used to generate representations of the simulated flows on a computer display unit. Photographs prepared from the displays illustrate the structure of the flows at the molecular level. The method has been applied to the steady hypersonic flow past circular cylinders, spheres, flat plates and blunt cones. These flows are represented either by several hundred typical molecular paths or by several thousand small arrows, each representing the position and velocity of a sample molecule at a particular instant. Colour was used to differentiate between undisturbed free-stream molecules, molecules that had struck the surface of the body and molecules that had been indirectly affected by the presence of the body. The method was also applied to the flow of a binary gas mixture past a circular cylinder, with colour used to differentiate between the components of the mixture.

An experiment is described which indicates a flow reversal due to fluid elasticity in the case of a rotating-plate experiment. An attempt to predict this reversal analytically on the ‘infinite’ plate assumption fails and recourse is made to a numerical procedure to solve the ‘finite’ plate problem. It is shown that the reversal is due to edge effects.

A linear theory is presented for the steady, axially symmetric motion of a stratified fluid in a narrow, rotating spherical annulus with a spherically symmetric gravitational field.

The fluid is driven by a combination of differential rotation of the two shells and differential heating applied at the surfaces of the spheres.

It is shown that the effect of stratification becomes increasingly important at lower latitudes with the Ekman layers on the spheres’ surfaces fading in strength as the geostrophic interior velocities themselves tend toward the shell speeds at lower latitudes.

The Singularities In The Geostrophic Solutions At The Equator Are Removed By A Boundary Layer Whose Detailed Structure Depends On The Ratio Of Horizontal To Vertical Mixing Coefficients Of Momentum And Heat.

A formal algebraic analogy is drawn between meteorological parameters, such as the Richardson number, and the parameters describing the effect of rotation or streamline curvature on a turbulent flow. The analogy between the phenomena is a good first approximation. Semi-quantitative use of the analogy to apply meteorological data to curved shear layers shows that the effects of curvature on the apparent mixing length are appreciable if the shear-layer thickness exceeds roughly 1/300 of the radius of curvature; larger effects may occur in compressible flow. Application of the Monin-Oboukhov formula considerably improves the agreement between prediction and experiment in boundary layers on curved surfaces.

The moment method proposed by Lees (1959) is applied to the problem of vapour condensation on and evaporation from spherical liquid droplets when the droplet is not in equilibrium with its surrounding. Using a four-moment solution, an analytical expression is derived for the mass flux to or from the droplet surface when the droplet is surrounded by a pure vapour. By neglecting changes in temperature, an analytical solution is also obtained for the mass flux when the droplet is immersed in a vapour-gas mixture. The results of both of these analyses are applicable in the range from λ/R → 0 to λ/R ∞, where λ is the mean free path and R the droplet radius, and it is shown that in the limits the results reduce to the appropriate free molecule and continuum expressions.

Sound generation by turbulent two-phase flow is considered by the methods of Lighthill's theory of aerodynamic noise. An inhomogeneous wave equation is derived, in which the effects of one phase on the other are represented by monopole, dipole and quadrupole distributions. The resulting power outputs are obtained for the case of a distribution of small air bubbles in water. The monopole radiation resulting from volumetric response of the bubbles to the turbulent pressure field overwhelms that from the quadrupoles equivalent to the turbulent flow, the increase in acoustic power output being about 70 dB for a volume concentration of 10%. The monopole radiation occurs through the forced response of the bubbles at the turbulence frequency; resonant response is shown to be impossible when the excitation is due to turbulence alone. Surface radiation arises from the edge of a cloud of bubbles. This radiation is important when the region containing bubbles is in the form of a sheet with thickness smaller than the length scale of the turbulent motion. Dipole radiation is also considered, and found to be negligible whenever monopole sources are present. In the case of a dusty gas, only dipole and quadrupole sources are present, and here it is shown that the dipole radiation is equivalent to an increase in the usual quadrupole radiation. The increase depends upon the mass concentration of dust, and is significant for mass concentrations in excess of unity.

In considering the onset of instability of an electrically conducting fluid between rotating permeable perfectly conducting cylinders in an applied axial magnetic field, it is found that oscillatory axially symmetric modes occur at large values of Hartmann number, in addition to the usual stationary modes. Results are presented showing the effect of the oscillatory modes on the criterion of onset of instability.

The asymptotic behaviour of the stability criterion is considered in the limit of very large radial Reynolds number, and also in the limit where both the radial Reynolds number and the Hartmann number are large.

The two-dimensional adiabatic transverse normal modes of an inviscid compressible fluid, having solid body rotation about the axis of its cylindrical container, are considered. Relative to the rotating fluid there are two trains of harmonic waves, propagating in opposite directions. The first five modes of the first-order harmonic wave and the first mode of the harmonic waves of order two, five, ten, fifteen and twenty have been considered. The period and amplitude of the waves is considerably modified by the rotation. Relative to a fixed coordinate system the angular velocity of the waves initially propagating in the same direction as the rotating fluid, is larger than that of the waves propagating in the opposite direction, as might be expected. However, in the case of the first mode, relative to the rotating fluid, the waves propagating in the opposite direction are the faster.

The stability of a horizontal layer of Maxwellian fluid heated from below is considered. Critical Rayleigh numbers, wave-numbers, and frequencies for overstability are determined for both free and rigid boundaries. Elasticity is found to destabilize the fluid, and the presence of rigid boundaries is found to be slightly stabilizing.